The dreidel is a traditional Hanukah toy. If the dreidel were merely a symbol of the Hanukah story then (borrowing from another holiday)-- Dayenu!--it would have been enough to assure its significance and memory throughout the generations. In fact, the dreidel has other symbolic meanings.
According to the American Heritage Dictionary of the English Language-Fourth Edition, the word dreidel derives from the Yiddish word dreydl based on dreyen, to turn. These words are themselves derived from Middle High German (draejen) and Old High German (draen). One occasionally sees alternative spellings dreidl, dreydl, and dreidyl in various contexts. More than one dreidel constitutes dreideloch but the common English plural is dreidels.
A dreidel differs from an ordinary spinning top because it is emblazoned with the four letters Nun-Gimel-Heh-Shin representing the words Nas-Godol-Hayah-Sham (A Great Miracle Happened There). Since 1948 Israeli dreidels bear the letters Nun-Gimel-Heh-Pei for the phrase A Great Miracle Happened Here.
The Hebrew word for dreidel is sivivon.
Physicists tell us that a spinning object generates an inertial torque that resists opposing motion. Spinning gyroscopes keep ships and planes on course. Whirling Dervishes spin themselves into a frenzy that they might enter a higher state of consciousness.
The dreidel is theology. The dreidel spins around a central point. It topples when it loses its connection to that point. So do we when we lose our Center. Spinning the dreidel is a symbol that life revolves about a Central Presence.
The dreidel is history. A dreidel has four sides. The four sides represent four empires that once enslaved us. The Babylonian, Persian, Greek and Roman empires each conquered most of the known world. In time they themselves toppled and fell.
The dreidel is psychology. A case can be made that the human spirit has four primary attributes: self (soul, nefesh), body (guf), reason (sechel) and everything (by extension, evil, hakol). When the dreidel is spun the four sides can no longer be distinguished and blend into a harmonious oneness about a single infinite point. Spinning the dreidel is a symbolic act of striving for that harmony.
The dreidel is philosophy. The four sides represent four aspects of the human dimension: that which stands apart (nivdal) the wheel of life (galgal), humility (shafal) and human potential (hiuli).
The dreidel is mystical numerology. Every Hebrew letter has an associated numerical value. Gematria assigns meanings to the arithmetic value of a word. Many congregations offer contributions in increments of $18 because the word chayim (life) has the numerical value eighteen.
The letters of the dreidel sum to 358, which is the same as the Hebrew word mashiach (Messiah). Spinning the dreidel is a symbolic act of messianic hope.
The letters in the Hebrew word for snake (nachash), also sum to 358.
The dreidel is Kabbalah geometry. The typical six-sided dreidel is related to a three dimensional projection of a torus in four-dimensional space. Followers of the Kabbalah assign mystical meanings to this geometric shape and its associated symmetries. It is said that if the each letter of the Hebrew alphabet were placed on a different vertex then various folds reveal combinations of letters spelling significant words.